Precalculus Examples

In simplest form, what is the slope of the line passing through $(5, 3)$ and $(- 4, - 3)$ ?

Step 1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 3 - (3)}{- 4 - (5)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $3$ .

$m = \frac{- 3 - 3}{- 4 - (5)}$

Step 4.1.2

Subtract $3$ from $- 3$ .

$m = \frac{- 6}{- 4 - (5)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $5$ .

$m = \frac{- 6}{- 4 - 5}$

Step 4.2.2

Subtract $5$ from $- 4$ .

$m = \frac{- 6}{- 9}$

Step 4.3

Cancel the common factor of $- 6$ and $- 9$ .

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Step 4.3.1

Factor $- 3$ out of $- 6$ .

$m = \frac{- 3 \cdot 2}{- 9}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $- 3$ out of $- 9$ .

$m = \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Step 4.3.2.2

Cancel the common factor.

$m = \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Step 4.3.2.3

Rewrite the expression.

$m = \frac{2}{3}$

Step 5